News of her departure comes just weeks after a lacklustre appearance before the House of Commons Public Accounts Committee which is investigating a series of higher than contracted payments to departing BBC bosses.
Committee Chair Margaret Hodge accused her of allowing “a huge amount of money” to be paid to departing managers instead of being spent on public service broadcasting.
In response, Adams conceded that “too often we were too generous”.
The grilling from MPs followed publication of a National Audit Office report which found the BBC broke its policies on severance pay “too often without good reason.
The report revealed that 150 departing BBC managers were paid £25m in the three years to December 2012, often pocketing tens of thousands of pounds instead of having to work notice periods.
During the period more than £3m was paid out in lieu of notice, including where some staff had secured paid employment before leaving the corporation.
In a statement, the BBC said Adams won’t receive a severance payment when she leaves next March.
Adams said she’d been discussing her future with BBC Director-General Tony Hall “for some time now”.
Hall, who joined the BBC in April, has pledged to clamp down on excesses at the BBC and has announced a cap on all future exit payments.
On Thursday Hall said he was “enormously grateful to Lucy for all her work and I will be very sorry to see her go next spring.”
He added: “She has done a great job and contributed a huge amount to the BBC. I am pleased that, in the short term at least, she will continue to help me simplify the way we do business in the BBC so that we can spend more time concentrating on our programmes and services.”